74 lines
3.3 KiB
TeX
74 lines
3.3 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\usepackage{booktabs}
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\title{Suites à connaître- Bilan}
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\date{Novembre 2019}
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\begin{document}
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\section*{Suites reconnaissables}
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\subsection*{Suites arithmétiques}
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Les \textbf{suites arithmétiques} modélisent les évolutions arithmétiques. On les reconnaît car pour passer d'un terme au suivant on ajoute (ou soustrait) toujours la même quantité appelée \textbf{raison} et notée $r$.
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=green!60, fill=green!5, very thick, minimum size=7mm},
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squarednode/.style={rectangle, draw=red!60, fill=red!5, very thick, minimum size=5mm},
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[1cm]{$u_0$}};
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\node[roundnode] (centerterm) [right=of leftterme] {\makebox[1cm]{$u_1$}};
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\node[roundnode] (rightterm) [right=of centerterm] {\makebox[1cm]{$u_2$}};
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\node[roundnode] (nthterm) [right=of rightterm] {\makebox[1cm]{$u_n$}};
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\node[roundnode] (nthplusterm) [right=of nthterm] {\makebox[1cm]{$u_{n+1}$}};
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%Lines
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\draw[->] (leftterme.east) -- (centerterm.west) node [midway, above] {+r};
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\draw[->] (centerterm.east) -- (rightterm.west) node [midway, above] {+r};
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\path (rightterm.east) -- (nthterm.west) node [midway] {...};
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\draw[->] (nthterm.east) -- (nthplusterm.west) node [midway, above] {+r};
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\end{tikzpicture}
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\end{center}
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Elles sont caractérisée par un premier terme $u_0$ et la relation de récurrence suivantes
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\[
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u_{n+1} = u_n + r
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\]
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\subsection*{Suites géométriques}
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Les \textbf{suites géométriques} modélisent les évolutions géométriques. On les reconnaît car pour passer d'un terme au suivant on multiplie (ou divise) toujours la même quantité appelée \textbf{raison} et notée $q$.
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=green!60, fill=green!5, very thick, minimum size=7mm},
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squarednode/.style={rectangle, draw=red!60, fill=red!5, very thick, minimum size=5mm},
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[1cm]{$u_0$}};
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\node[roundnode] (centerterm) [right=of leftterme] {\makebox[1cm]{$u_1$}};
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\node[roundnode] (rightterm) [right=of centerterm] {\makebox[1cm]{$u_2$}};
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\node[roundnode] (nthterm) [right=of rightterm] {\makebox[1cm]{$u_n$}};
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\node[roundnode] (nthplusterm) [right=of nthterm] {\makebox[1cm]{$u_{n+1}$}};
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%Lines
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\draw[->] (leftterme.east) -- (centerterm.west) node [midway, above] {$\times q$};
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\draw[->] (centerterm.east) -- (rightterm.west) node [midway, above] {$\times q$};
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\path (rightterm.east) -- (nthterm.west) node [midway] {...};
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\draw[->] (nthterm.east) -- (nthplusterm.west) node [midway, above] {$\times q$};
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\end{tikzpicture}
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\end{center}
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Elles sont caractérisée par un premier terme $u_0$ et la relation de récurrence suivantes
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\[
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u_{n+1} = u_n \times q
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\]
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\subsection*{Remarque}
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Dans son chapitre, on a rencontré des suites qui n'étaient ni arithmétique ni géométrique.
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\end{document}
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